limited accuracy for tanh-sinh integrator

From: Anirban Pal (anirban.pal.iitkgp_at_[hidden])
Date: 2020-08-16 20:15:14

Hello,

I’m using the tanh-sinh integrator to integrate a simple function f(x) =
0.26*x from 3.0 to 4.0.
The exact result is 0.91. With the integrator I’m getting a result accurate
to only 10^-18 with cpp_bin_float_100 multiprecision.

typedef boost::multiprecision::cpp_bin_float_100 Real;

int main(int argc, char **argv)
{
    using namespace boost::math::quadrature;
    using namespace std::placeholders;
    tanh_sinh<Real> integrator;

    auto f2 = [](Real x) {
        Real a = 0.26;
        return x*a;

    };

    std::cout << std::setprecision(std::numeric_limits<Real>::max_digits10)
     << "Comp.: " << integrator.integrate(f2, (Real) 3.0, (Real) 4.0)
<< std::endl;

    return 0;
}

I'm getting an output of

Comp.:
0.9100000000000000310862446895043831318616867065429687499999999999999999999999999999999999999999999999429

which I'm a bit curious about. I was wondering if I can improve the result.

Thank you.

-- 
Anirban Pal